On I- Convergence of Sequences in Gradual Normed Linear Spaces

Abstract

In this paper, we introduce the concepts of $\mathcal{I}$ and $\mathcal{I^{*}}-$convergence of sequences in gradual normed linear spaces. We study some basic properties and implication relations of the newly defined convergence concepts. Also, we introduce the notions of $\mathcal{I}$ and $\mathcal{I^{*}}-$Cauchy sequences in the gradual normed linear space and investigate the relations between them.

CERTAIN ASPECTS OF Xrst(G)-CONVERGENCE OF SEQUENCES IN GRADUAL NORMED LINEAR SPACES

“…They studied various properties from both the algebraic and topological points of view. Further development in this direction has been taken place due to Ettefagh et al [20,21], Choudhury and Debnath [13,14], and many others. For an extensive study on gradual real numbers, one may refer to [1,18,28,36].…”

On lacunary statistical convergence of sequences in gradual normed linear spaces

“…Also, they have investigated some properties from the topological point of view [6]. In [2], Choudhury and Debnath have generalized the notion of convergence of sequences in the gradual normed linear spaces to ideal convergence. Therefore, the study of lacunary statistical convergence of sequences in gradual normed linear spaces is very natural.…”

Rough I_((λ,μ) )-Statistical Convergence of Double Sequences in Gradual Normed Linear Spaces

“…They worked various properties from both the topological and algebraic points of view. Further development in this direction has been taken place due to Choudhury and Debnath [3], Ettefagh et. al.…”